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Question 1 Consider the function f: R→R, given by -((m + 1) -mx) (x+1), C (a) Find the y intercept of f(x). (b) Find the intercepts of f(r). As nessessary give the answers as a fraction and as a decimal rounded to the first decimal place. (e) Find the first two derivatives of f(r), i.e. find f'(z), f"(x). (d) Find the stationary points of f(r) (r- and y-coordinates of stationary points, rounded to the first decimal place) and determine whether they are minima, maxima, or neither. (e) Are there any points of inflection of function f? If so, identify them (rounded to the first decimal place) and state the interval(s), where f is concave up and the interval(s) where fis concave down. If f does not have any points of inflection, determine whether f is concave up or down on the domain.

Question 1 Consider the function f: R→R, given by -((m + 1) -mx) (x+1), C (a) Find the y intercept of f(x). (b) Find the intercepts of f(r). As nessessary give the answers as a fraction and as a decimal rounded to the first decimal place. (e) Find the first two derivatives of f(r), i.e. find f'(z), f"(x). (d) Find the stationary points of f(r) (r- and y-coordinates of stationary points, rounded to the first decimal place) and determine whether they are minima, maxima, or neither. (e) Are there any points of inflection of function f? If so, identify them (rounded to the first decimal place) and state the interval(s), where f is concave up and the interval(s) where fis concave down. If f does not have any points of inflection, determine whether f is concave up or down on the domain.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 59CR
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I attached the 3 parts you have to solve the last three parts d, e and f Use m=3
Question 1 Consider the function f: R→ R, given by f(x) = ((m + 1) -mx) (x + 1), (+) (a) Find the y intercept of f(x). (b) Find the z intercepts of f(x). As nessessary give the answers as a fraction and as a decimal rounded to the first decimal place. (c) Find the first two derivatives of f(x), i.e. find f'(x), f"(r). (d) Find the stationary points of f(x) (r- and y-coordinates of stationary points, rounded to the first decimal place) and determine whether they are minima, maxima, or neither. (e) Are there any points of inflection of function f? If so, identify them (rounded to the first decimal place) and state the interval(s), where f is concave up and the interval(s) where fis concave down. If f does not have any points of inflection, determine whether f is concave up or down on the domain. (f) Using the results from the parts (a) -(e) sketch the graph of f (per hand). Label all feature points that you have found in parts (b)-(e). Make sure your graphs are large, typically each graph should be roughly square and at least a third of the width of the page. For sketching the graph, do not use a graphical calculator or a computer software.
Transcribed Image Text:Question 1 Consider the function f: R→ R, given by f(x) = ((m + 1) -mx) (x + 1), (+) (a) Find the y intercept of f(x). (b) Find the z intercepts of f(x). As nessessary give the answers as a fraction and as a decimal rounded to the first decimal place. (c) Find the first two derivatives of f(x), i.e. find f'(x), f"(r). (d) Find the stationary points of f(x) (r- and y-coordinates of stationary points, rounded to the first decimal place) and determine whether they are minima, maxima, or neither. (e) Are there any points of inflection of function f? If so, identify them (rounded to the first decimal place) and state the interval(s), where f is concave up and the interval(s) where fis concave down. If f does not have any points of inflection, determine whether f is concave up or down on the domain. (f) Using the results from the parts (a) -(e) sketch the graph of f (per hand). Label all feature points that you have found in parts (b)-(e). Make sure your graphs are large, typically each graph should be roughly square and at least a third of the width of the page. For sketching the graph, do not use a graphical calculator or a computer software.
Therefore, (a) The y intercept is (0,4) (b) The x intercepts are (-1,0) and (₂0) = (1-3,0). (Ⓒ) f'(x) = -ex (4-3x) (x+1) - 3ē*(x+1) +ex (x+1). f"(x) = x (1-3x) (x+1) + 60x²(x+1) -2ex (1-3x) -6e-x
Transcribed Image Text:Therefore, (a) The y intercept is (0,4) (b) The x intercepts are (-1,0) and (₂0) = (1-3,0). (Ⓒ) f'(x) = -ex (4-3x) (x+1) - 3ē*(x+1) +ex (x+1). f"(x) = x (1-3x) (x+1) + 60x²(x+1) -2ex (1-3x) -6e-x
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